Basic Math Examples

$\frac{15 u^{6} z - 21 u^{6} z^{7} + 7 u^{6} z^{5}}{- 3 u^{5} z^{4}}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $u^{6} z$ out of $15 u^{6} z - 21 u^{6} z^{7} + 7 u^{6} z^{5}$ .

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Step 1.1.1

Factor $u^{6} z$ out of $15 u^{6} z$ .

$\frac{u^{6} z (15) - 21 u^{6} z^{7} + 7 u^{6} z^{5}}{- 3 u^{5} z^{4}}$

Step 1.1.2

Factor $u^{6} z$ out of $- 21 u^{6} z^{7}$ .

$\frac{u^{6} z (15) + u^{6} z (- 21 z^{6}) + 7 u^{6} z^{5}}{- 3 u^{5} z^{4}}$

Step 1.1.3

Factor $u^{6} z$ out of $7 u^{6} z^{5}$ .

$\frac{u^{6} z (15) + u^{6} z (- 21 z^{6}) + u^{6} z (7 z^{4})}{- 3 u^{5} z^{4}}$

Step 1.1.4

Factor $u^{6} z$ out of $u^{6} z (15) + u^{6} z (- 21 z^{6})$ .

$\frac{u^{6} z (15 - 21 z^{6}) + u^{6} z (7 z^{4})}{- 3 u^{5} z^{4}}$

Step 1.1.5

Factor $u^{6} z$ out of $u^{6} z (15 - 21 z^{6}) + u^{6} z (7 z^{4})$ .

$\frac{u^{6} z (15 - 21 z^{6} + 7 z^{4})}{- 3 u^{5} z^{4}}$

Step 1.2

Reorder terms.

$\frac{u^{6} z (- 21 z^{6} + 7 z^{4} + 15)}{- 3 u^{5} z^{4}}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $u^{6}$ and $u^{5}$ .

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Step 2.1.1

Factor $u^{5}$ out of $u^{6} z (- 21 z^{6} + 7 z^{4} + 15)$ .

$\frac{u^{5} (u z (- 21 z^{6} + 7 z^{4} + 15))}{- 3 u^{5} z^{4}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $u^{5}$ out of $- 3 u^{5} z^{4}$ .

$\frac{u^{5} (u z (- 21 z^{6} + 7 z^{4} + 15))}{u^{5} (- 3 z^{4})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{u^{5} (u z (- 21 z^{6} + 7 z^{4} + 15))}{u^{5} (- 3 z^{4})}$

Step 2.1.2.3

Rewrite the expression.

$\frac{u z (- 21 z^{6} + 7 z^{4} + 15)}{- 3 z^{4}}$

Step 2.2

Cancel the common factor of $z$ and $z^{4}$ .

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Step 2.2.1

Factor $z$ out of $u z (- 21 z^{6} + 7 z^{4} + 15)$ .

$\frac{z (u (- 21 z^{6} + 7 z^{4} + 15))}{- 3 z^{4}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $z$ out of $- 3 z^{4}$ .

$\frac{z (u (- 21 z^{6} + 7 z^{4} + 15))}{z (- 3 z^{3})}$

Step 2.2.2.2

Cancel the common factor.

$\frac{z (u (- 21 z^{6} + 7 z^{4} + 15))}{z (- 3 z^{3})}$

Step 2.2.2.3

Rewrite the expression.

$\frac{u (- 21 z^{6} + 7 z^{4} + 15)}{- 3 z^{3}}$

Step 2.3

Move the negative in front of the fraction.

$- \frac{u (- 21 z^{6} + 7 z^{4} + 15)}{3 z^{3}}$

Step 2.4

Factor $- 1$ out of $- 21 z^{6}$ .

$- \frac{u (- (21 z^{6}) + 7 z^{4} + 15)}{3 z^{3}}$

Step 2.5

Factor $- 1$ out of $7 z^{4}$ .

$- \frac{u (- (21 z^{6}) - (- 7 z^{4}) + 15)}{3 z^{3}}$

Step 2.6

Factor $- 1$ out of $- (21 z^{6}) - (- 7 z^{4})$ .

$- \frac{u (- (21 z^{6} - 7 z^{4}) + 15)}{3 z^{3}}$

Step 2.7

Rewrite $15$ as $- 1 (- 15)$ .

$- \frac{u (- (21 z^{6} - 7 z^{4}) - 1 (- 15))}{3 z^{3}}$

Step 2.8

Factor $- 1$ out of $- (21 z^{6} - 7 z^{4}) - 1 (- 15)$ .

$- \frac{u (- (21 z^{6} - 7 z^{4} - 15))}{3 z^{3}}$

Step 2.9

Simplify the expression.

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Step 2.9.1

Rewrite $- (21 z^{6} - 7 z^{4} - 15)$ as $- 1 (21 z^{6} - 7 z^{4} - 15)$ .

$- \frac{u (- 1 (21 z^{6} - 7 z^{4} - 15))}{3 z^{3}}$

Step 2.9.2

Move the negative in front of the fraction.

$- - \frac{u (21 z^{6} - 7 z^{4} - 15)}{3 z^{3}}$

Step 2.9.3

Multiply $- 1$ by $- 1$ .

$1 \frac{u (21 z^{6} - 7 z^{4} - 15)}{3 z^{3}}$

Step 2.9.4

Multiply $\frac{u (21 z^{6} - 7 z^{4} - 15)}{3 z^{3}}$ by $1$ .

$\frac{u (21 z^{6} - 7 z^{4} - 15)}{3 z^{3}}$